I see several knowledgeable members refer to rod rating with numbers when giving recommendations. I wish I fully understood what the numbers mean.
 

Is there a handy reference for numeric equivalents on the “Ultralight, Light, Medium Light, Medium, Medium Heavy, Heavy, X-Heavy” spectrum? Or is there a different, better way to understand this?

 

Finally, are these any different than ratings for fly rods, for which numeric “weight” ratings are the norm?

You might be referring to the common cents system, developed 20+ years ago now, initially for fly rods but equally applicable to all types of rods.  Read through the CC pages below and that should help. 
 

https://www.common-cents.info

the problem with aftma fly rod ratings is explained in the common cents pages. While there is a numerical rating that is supposed to correspond to a weigh range, it’s not used the same by all manufacturers so one company’s 6 weight is another company’s 5 weight distance casting rod. With a numerical measurement like the CC system, there is no subjective evaluation. 

 

Common Cents is a replacement for subjective terms not a definition of them. Rod ratings used by manufacturers are totally subjective with no industry standard or definition.  The best way to get any understanding is to read the power rating and associated lure weight and line # ratings of different power rods from different manufacturers and models within manufacturers. Only with familiarity and experience will you begin to get any understanding. You’ll hear opinions of who makes a “true med Hvy” etc but there is no such thing. 

If it wasn’t for the input by members here on BR, there would be a bunch of anglers with bald spots from scratching their heads trying to affirm what rod company’s ratings are accurate.  If you can figure this out, the next step is to determine if the progression of the “powers” are consistent.  

And furthermore, a mh graphite is surely not the same as a mh glass. The only thing that's pretty consistent is a manufacturers rods are consistent within their own lines.

1 hour ago, JediAmoeba said:

The only thing that's pretty consistent is a manufacturers rods are consistent within their own lines.

 

For me, this is one reason why I stick with Falcon rods.  Aside from them being great rods and fitting my preferences, I've fished enough of them now that I can predict pretty closely what a falcon is going to feel like in my hand based on the rating and description.  That helps a ton when you aren't buying in person.